A reaction–diffusion model of the Darien Gap Sterile Insect Release Method

Alford, John G.

doi:10.1016/j.cnsns.2014.10.004

Cited by 8 publications

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This theme has traditionally been addressed from the establishment of conservation equations that take into account the factors that affect the size of the population studied. Thus we arrive at the reaction-diffusion equations (RDE), which describe the temporal evolution of the population density

in the form [3]

These equations frequently appear in the study of systems of the most diverse nature [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] , [28] , [29] , [30] , [31] , [32] , [33] , [34] , [35] , [36] , [37] , [38] , [39] , [40] , [41] , [42] , [43] , [44] , [45] , [46] , [47] , [48] , leading to interesting phenomena, such as critical behavior, multiple stationary states, spatial patterns, wave fronts and oscillations. Here Γ is the source term, whose specific form will depend on the problem under study.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Aranda

Penna

Oliveira

2021

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

Highlights It is proposed a model based on non-local operators capable of reproduce several of the equations traditionally used in research on population dynamics, as well as having additional features, useful for describing the phenomenon of pattern formation. The combination of two of the parameters present in the model, namely, α and β , determines the existence of a phase space, characterized by regions with and without patterns. The patterns formed will have M peaks and M valleys, with M ≥ 2. There are ( α, β ) combinations which lead to the formation of degenerate states, where the system seems not to forget its initial conditions. The model allows the study of real systems, such is the case of bacterial populations subjected to inhomogeneous growth conditions. The parameter β represents a macroscopic measure of changes that occur at an individual level in the concentrations of proteins in bacteria, as a product of significant variations in the environment.

show abstract

in the form [3]

Section: Introductionmentioning

confidence: 99%

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Aranda

Penna

Oliveira

2021

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

show abstract

Competitive Exclusion and Axiomatic Set-Theory: De Morgan’s Laws, Ecological Virtual Processes, Symmetries and Frozen Diversity

Flores

2016

Acta Biotheor

View full text Add to dashboard Cite

This work applies the competitive exclusion principle and the concept of potential competitors as simple axiomatic tools to generalized situations in ecology. These tools enable apparent competition and its dual counterpart to be explicitly evaluated in poorly understood ecological systems. Within this set-theory framework we explore theoretical symmetries and invariances, De Morgan's laws, frozen evolutionary diversity and virtual processes. In particular, we find that the exclusion principle compromises the geometrical growth of the number of species. By theoretical extending this principle, we can describe interspecific depredation in the dual case. This study also briefly considers the debated situation of intraspecific competition. The ecological consequences of our findings are discussed; particularly, the use of our framework to reinterpret coupled mathematical differential equations describing certain ecological processes.

show abstract

Diffusing wild type and sterile mosquitoes in an optimal control setting

Fister

McCarthy

Oppenheimer

2018

Mathematical Biosciences

View full text Add to dashboard Cite

This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations.

show abstract

A reaction–diffusion model of the Darien Gap Sterile Insect Release Method

Cited by 8 publications

References 14 publications

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Competitive Exclusion and Axiomatic Set-Theory: De Morgan’s Laws, Ecological Virtual Processes, Symmetries and Frozen Diversity

Diffusing wild type and sterile mosquitoes in an optimal control setting

Contact Info

Product

Resources

About